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Ward identities and consistency relations for the large scale structure with multiple species
"... We present fully nonlinear consistency relations for the squeezed bispectrum of Large Scale Structure. These relations hold when the matter component of the Universe is composed of one or more species, and generalize those obtained in [1, 2] in the single species case. The multispecies relations ap ..."
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We present fully nonlinear consistency relations for the squeezed bispectrum of Large Scale Structure. These relations hold when the matter component of the Universe is composed of one or more species, and generalize those obtained in [1, 2] in the single species case. The multispecies relations apply to the standard dark matter + baryons scenario, as well as to the case in which some of the fields are auxiliary quantities describing a particular population, such as dark matter halos or a specific galaxy class. If a large scale velocity bias exists between the different populations new terms appear in the consistency relations with respect to the single species case. As an illustration, we discuss two physical cases in which such a velocity bias can exist: (1) a new long range scalar force in the dark matter sector (resulting in a violation of the equivalence principle in the dark matterbaryon system), and (2) the distribution of dark matter halos relative to that of the underlying dark matter field. ar X iv
Inflationary tensor fossils in largescale structure,” arXiv:1407.8204 [astroph.CO
"... Abstract. Inflation models make specific predictions for a tensorscalarscalar threepoint correlation, or bispectrum, between one gravitationalwave (tensor) mode and two densityperturbation (scalar) modes. This tensorscalarscalar correlation leads to a local power quadrupole, an apparent depar ..."
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Abstract. Inflation models make specific predictions for a tensorscalarscalar threepoint correlation, or bispectrum, between one gravitationalwave (tensor) mode and two densityperturbation (scalar) modes. This tensorscalarscalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic fourpoint correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for singleclock models in which certain consistency conditions between the tensorscalarscalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to be satisfied. We then consider several examples of inflation models, such as nonattractor and solidinflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the nonattractor model we find that, contrary to the standard scenario, the tensorscalarscalar correlator probes directly relevant modeldependent information. We work out the predictions for observables in these models. For nonattractor inflation we find an apparent local quadrupolar departure from statistical isotropy in largescale structure but that this
SlavnovTaylor Identities for Primordial Perturbations
, 2014
"... Correlation functions of adiabatic modes in cosmology are constrained by an infinite number of consistency relations, which relate N + 1point correlation functions with a softmomentum scalar or tensor mode to a symmetry transformation on Npoint correlation functions of hardmomentum modes. They c ..."
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Correlation functions of adiabatic modes in cosmology are constrained by an infinite number of consistency relations, which relate N + 1point correlation functions with a softmomentum scalar or tensor mode to a symmetry transformation on Npoint correlation functions of hardmomentum modes. They constrain, at each order n, the qn behavior of the soft limits. In this paper we show that all consistency relations derive from a single, master identity, which follows from the SlavnovTaylor identity for spatial diffeomorphisms. This master identity is valid at any value of q and therefore goes beyond the soft limit. By differentiating it n times with respect to the soft momentum, we recover the consistency relations at each q order. Our approach underscores the role of spatial diffeomorphism invariance at the root of cosmological consistency relations. It also offers new insights on the necessary conditions for their validity: a physical contribution to the vertex functional must satisfy certain analyticity properties in the soft limit in order for the consistency relations to hold. For standard inflationary models, this is equivalent to requiring that mode functions have constant growingmode solutions. For more exotic models in which modes do not “freeze ” in the usual sense, the analyticity requirement offers an unambiguous criterion.
Consistency Relations for the Conformal Mechanism
, 2013
"... We systematically derive the consistency relations associated to the nonlinearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearlyrealized de Sitter subalgebra. These identities relate (N+1)point correlation functions with a soft external Goldstone t ..."
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We systematically derive the consistency relations associated to the nonlinearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearlyrealized de Sitter subalgebra. These identities relate (N+1)point correlation functions with a soft external Goldstone to Npoint functions. These relations have direct implications for the recently proposed conformal mechanism for generating density perturbations in the early universe. We study the observational consequences, in particular a novel oneloop contribution to the fourpoint function, relevant for the stochastic scaledependent bias and CMB µdistortion.
Consistency Relations for the Conformal Mechanism
"... We systematically derive the consistency relations associated to the nonlinearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearlyrealized de Sitter subalgebra. These identities relate (N+1)point correlation functions with a soft external Goldstone t ..."
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We systematically derive the consistency relations associated to the nonlinearly realized symmetries of theories with spontaneously broken conformal symmetry but with a linearlyrealized de Sitter subalgebra. These identities relate (N+1)point correlation functions with a soft external Goldstone to Npoint functions. These relations have direct implications for the recently proposed conformal mechanism for generating density perturbations in the early universe. We study the observational consequences, in particular a novel oneloop contribution to the fourpoint function, relevant for the stochastic scaledependent bias and CMB µdistortion. 1
TABLE OF CONTENTS
"... Abstract—This paper presents the design characterization of a heterogeneous sensor network with the goal of geolocation accuracy. It is assumed that the network exploits sensor management to conserve node usage. Each available node modality is a bearingsonly sensor of varying capability. The optima ..."
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Abstract—This paper presents the design characterization of a heterogeneous sensor network with the goal of geolocation accuracy. It is assumed that the network exploits sensor management to conserve node usage. Each available node modality is a bearingsonly sensor of varying capability. The optimal mixture of modalities is discussed under the constraint of the overall network cost. Finally, simulations verify the theory and demonstrate design choices for a network consisting
A Consistency Relation for the CMB Bmode Polarization in the Squeezed Limit
"... A largescale temperature perturbation has a nonzero correlation with the power spectrum of Bmodes of cosmological origin on short scales while the corresponding correlation is expected to be zero for Bmodes sourced by galactic foregrounds. We thus compute the squeezed limit of a threepoint func ..."
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A largescale temperature perturbation has a nonzero correlation with the power spectrum of Bmodes of cosmological origin on short scales while the corresponding correlation is expected to be zero for Bmodes sourced by galactic foregrounds. We thus compute the squeezed limit of a threepoint function in which one correlates the temperature fluctuations at large scales with two polarization modes at small scales. In the particular case of the Bmode polarization we obtain a relation that connects the squeezed limit of the TBB threepoint function with the cosmological Bmode power spectrum, which can be used as a consistency relation. This could in principle help to distinguish a primordial signal from that induced by interstellar dust. 1